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Center for Biomedical Engineering, University of Kentucky, Lexington, Kentucky
Submitted 5 February 2008 ; accepted in final form 23 June 2008
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ABSTRACT |
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 TOP ABSTRACT GlossaryMETHODSStatisticsTheory and Analysis of...RESULTSDISCUSSIONGRANTSREFERENCES |
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airway resistance; barometric plethysmography; end-expiratory volume; tidal volume; limiting diameter
The goals of the present study were twofold. First, we studied the changes in VE, tidal volume (VT), and Raw in response to graded doses of 25, 50, and 100 mg/ml MCh aerosol rather than the single dose between 50 and 125 mg/ml used previously (20). Second, we developed a more direct measure of the airway response to MCh to validate the changes in Raw calculated using barometric plethysmography. We insufflated tantalum dust into the airways of anesthetized mice, and, after recovery from the anesthesia, we measured airway caliber from tantalum bronchograms collected in the conscious mice. We determined the response in both lung volume and airway caliber to graded doses of MCh aerosol. In contrast to the previous study (20), Raw doubled in response to MCh from control values measured after tantalum dust exposure, and this behavior pointed to tantalum dust-induced changes in Raw. The results indicated a monotonic decrease in airway caliber simultaneously with an increase in the mean lung volume to limiting values with 100 mg/ml MCh.
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Glossary |
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TOPABSTRACTGlossaryMETHODSStatisticsTheory and Analysis of...RESULTSDISCUSSIONGRANTSREFERENCES |
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PbPb
Pel
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METHODS |
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TOPABSTRACTGlossaryMETHODSStatisticsTheory and Analysis of...RESULTSDISCUSSIONGRANTSREFERENCES |
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30 mg of the dust were insufflated into the lungs by a rapid 0.2-ml air injection. An X-ray image of the thorax using a 10-ms pulse exposure from an X-ray generator (20) confirmed an acceptable distribution of dust within the airways (Fig. 1).
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In brief, the plethysmograph consisted of a transparent plastic tube of a diameter small enough to prevent the mouse from turning around (20). The cone-shaped end of the tube interfaced to a copper cylinder with connecting holes drilled in the cone. The head of the mouse was located at the cone-shaped end. A pressure transducer, humidity and temperature probe, and CO2 probe were located near the cone-shaped end. A silicon rubber heater bonded to the outside of the copper cylinder, together with an external infrared lamp and thermostatic controller, provided heat to the box to maintain the box air temperature at 37°C, as needed in the experiments. An aerosolyzer provided either saline or MCh aerosol at 100% relative humidity with an airflow of 10 l/min. An X-ray generator with a 1.8-mm focal spot provided a single 10-ms pulse at 80 kV and 15 mA (Bowie Manufacturing, model PRX-90T). Digital X-ray images were collected on a PC using a digital X-ray sensor (4.2 x 3 cm) with commercial software (Lightyear Technology). Source-to-sensor distance was 24 cm, and lung-to-sensor distance was 0.5–1.0 cm. Correction for magnification was <5%. Lung and heart area, heart area, and airway diameter (D) were measured from the X-ray images using commercial software (Photoshop and NIH image) on a PC.
With the box sealed, Pb excursions, box air temperature, and humidity were measured, and X-ray images of the thorax were taken at several maximum and minimum points of sequential Pb cycles. Measurements for control conditions breathing humidified saline aerosol and after 1-min exposures to 25, 50, and 100 mg/ml MCh aerosol were made. The 100 mg/ml MCh aerosol exposure was repeated twice. The time period between the MCh exposures when the box was sealed was 2–4 min. The entire experiment lasted 35 min. Airflow with the MCh aerosol through the box during the 1-min exposures prevented the accumulation of CO2 before sealing.
On the following day, Pb excursions and X-rays were measured with the conscious mouse in the box filled with room temperature air humidified with saline aerosol. Then the box air was heated and stabilized to 37°C for 1 h using a previous procedure (20). Pb and X-rays were measured after placing the mouse in the heated box at 37°C and 100% relative humidity. X-ray images were taken at maximum and minimum points of the pressure cycle with room temperature box air and at midpoints between maximum and minimum points of the pressure cycles under body temperature box air conditions. X-rays were taken with a single 10-ms pulse that provided the temporal resolution (100 Hz) required to produce sharp images of the lungs of conscious mice breathing at 5 Hz (20).
After the foregoing studies, each mouse was euthanized with an overdose of pentobarbital sodium (200 mg/kg injected ip), followed by exsanguination. The trachea was cannulated, and the chest opened by a midline sternotomy to expose the lung pleural surfaces to ambient pressure. The lungs were inflated to 25- to 30-cmH2O transpulmonary pressure [Ptp; airway pressure (Paw) relative to pleural pressure (Ppl), which was atmospheric] with a syringe and deflated to 0-cmH2O Ptp in 0.1-ml volume increments. The equilibrated Ptp after each increment was recorded. This procedure was repeated three times, and the third time was used for the pressure-volume (P-V) behavior. The collapsed lung was weighed and displaced in water to determine its total displaced volume and the trapped gas volume. The lungs were air dried at 25-cmH2O Ptp and subsequently examined for tantalum dust trapped on the subpleural alveolar surfaces. The lung was dried to a constant weight to determine its wet-to-dry weight ratio.
In separate experiments, we repeated the foregoing studies with doses of 25, 100, 150, and 250 mg/ml MCh to determine whether higher doses affected the response in D and lung volume observed with 100 mg/ml MCh.
The corrected lung area (AL) of each X-ray image was measured by subtracting the heart area from the area of the lung including the heart (20). The total lung volume (VL) was assumed to be uniformly inflated and related to AL according to the following equation:
 | (1) |
D was measured from the tantalum bronchograms observed on the X-ray images. Because the orientation of the chest of the conscious mouse changed slightly among X-ray images, the locations of airway branches were not always superimposed. Thus to compare D among the X-ray images, we chose segments between branches of approximately the same location and length from each X-ray image and divided segment area by segment length to obtain a mean segment diameter (Fig. 1). Area and length of each segment were measured three times and averaged to reduce errors due to resolution (100 µm). Because of resolution errors, only D values >0.3 mm were selected. Segment length was 1 mm. With this procedure, mean segment diameter (0.61 mm) was measured to within 15% error. From each X-ray image, we chose three to four airway segments and obtained an average segmental diameter. The airways measured were confined to the first five generations, and the trachea was excluded.
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Statistics |
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Theory and Analysis of Data |
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TOPABSTRACTGlossaryMETHODSStatisticsTheory and Analysis of...RESULTSDISCUSSIONGRANTSREFERENCES |
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The method to evaluate Raw using barometric plethysmography requires the Pb excursion, lung VT and VE, under both room temperature and body temperature box air conditions. A detailed description has been published (20, 21). In brief, for an animal breathing spontaneously in a sealed box, Raw is given by the equation:
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Pb, Pg, and Ph is:
 | (3) |
between Pb and Ph is given by:
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Pb was taken as one-half the peak-to-peak Pb excursion (Pb), and Abt was the average of the areas under the inspiratory and expiratory parts of the Pg vs. t curve, equal to Pg/(
f) for a sine wave with frequency f. Phase difference between Pb and VL.
Drorbaugh and Fenn (5) showed that the inspired gas volume dVL is proportional to dPh; thus VL is related in phase to Pb as Ph (Eq. 4). VL was measured at maximum and minimum points of the Pb cycle and corrected for phase to determine VL at end inspiration and end expiration and VT. For control (unconstricted) conditions (subscript 1), 1 was calculated using Eq. 4 with Ph1/Pg1 determined from the equation (cf. Eq. 14 of Ref. 21):
 | (5) |
Pb1 and Pg1 are the Pb amplitudes measured with room temperature and body temperature humidified box air conditions, respectively. Calculation of VT, total Vm, Vm, and VE.
The VL measured at the maximum (VLmax) and minimum (VLmin) points of the Pb excursion provided an estimate of VT with a correction for phase (20):
 | (6) |
 | (7) |
Determination of VT and VLm after bronchoconstriction due to MCh aerosol exposure.
The determination of VT2 for the bronchoconstricted animals required its simultaneous solution with Pg2. Subscript 2 refers to constricted conditions. We used the following procedure. We obtained unique solutions for VT2/VT1 (that is, Ph2/Ph1) and Pg2/Pg1 from the experimental data as follows. First, starting with a trial value of VT2/VT1 and Ph1/Pg1 known from control conditions (Eq. 5), Pg2/Pg1 was calculated using the following equation (Eq. 19 of Ref. 21), obtained by applying Eq. 3 to control and constricted conditions:
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Ph2/Pg2 was calculated using the product of the three ratios:
 | (9) |
2 was computed using Eq. 4. Fourth, the predicted VT2 and VLm2 values were calculated using measured VL2max and VL2min values and computed 2 value in Eqs. 6 and 7. The trial VT2/VT1 was varied to match the predicted VT2/VT1 to produce unique solutions for Pg2/Pg1, VT ratio, and Vm ratio after correction for tissue and blood mass. Raw ratio with MCh was obtained by applying Abt ratio equal to Pg/f ratio, and VT and Vm ratios to Eq. 2. |
RESULTS |
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TOPABSTRACTGlossaryMETHODSStatisticsTheory and Analysis of...RESULTSDISCUSSIONGRANTSREFERENCES |
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Pb, Ph/Pg, , Pg, f, Abt, and Raw for control conditions and after exposure to MCh aerosol (100 mg/ml). Control VT values [0.31 ± 0.068 ml (SD), n = 6] calculated using the Pb excursions and corrected for gas compression effects by multiplying by cos 1 were not significantly different from VT (0.28 ± 0.051 ml) calculated from the X-ray data using Eq. 6. Raw averaged 1.7 ± 0.70 cmH2O·ml–1·s under control conditions and doubled with the 100 mg/ml MCh exposure. The response to 100 mg/ml MCh was to increase VE 2.2-fold and to decrease f by 35%, with no change in VT. Data for the three 100 mg/ml MCh aerosol exposures were similar and averaged.
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Figure 4 shows the deflation P-V behavior of the isolated lungs measured postmortem. Lung air volume (V) included the trapped air volume measured by water displacement. The best fit parabola to the data was: V = –0.0012 Ptp2 + 0.078 Ptp + 0.21, R2 = 0.99. Based on the P-V behavior, the control Vm of 0.58 ml and control VE of 0.44 ml (Table 1) were equivalent to Ptp values in vivo of 5 and 3 cmH2O, respectively. Vm and VE values of 0.97 and 0.80 ml, the maximum values with 100 mg/ml MCh, were associated with Ptp values of 12 and 8.6 cmH2O, respectively. These Ptp values were close to those required to prevent airway closure in excised and intact dog lungs (Ref. 13, 41; see DISCUSSION).
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DISCUSSION |
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TOPABSTRACTGlossaryMETHODSStatisticsTheory and Analysis of...RESULTSDISCUSSIONGRANTSREFERENCES |
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Methods
The study of the bronchial response to MCh was limited to within 1 day after the application of the tantalum dust. The ability to measure airway caliber from tantalum bronchograms in response to MCh aerosol in conscious mice depended on both the amount of dust insufflated and on the subsequent clearance of the dust. There were several factors that proved critical. First, too much dust insufflated prevented the recovery of the mouse from the anesthesia and, on one occasion, resulted in the death of the animal. Too much dust also masked the heart area and diaphragm outlines that were needed for the lung volume measurements from the X-ray images (20). Too little dust insufflated was cleared too quickly during the overnight recovery of the animal and produced degraded bronchograms that prevented accurate measurements of airway caliber. In addition, too much dust deposited on the airway lumen might also reduce the absorption of the MCh into the airway smooth muscle and the bronchoconstriction response. Second, some dust on insufflation was deposited in the alveolar compartment. This was evident from the tantalum dust observed through the pleural surface of the lungs after opening the chest and of the isolated lungs air-dried 3–4 days after the dust insufflation.
The tantalum bronchographic method has been used extensively in large experimental animals (8, 15, 16, 22, 25, 31, 35), and tantalum dust clearance from the lung in these studies ranges from a few hours (22, 31) to months (8). There is a paucity of similar studies in rodents (37). The long-term pathological effects of the tantalum dust that is deposited on alveolar surfaces and not cleared by airway mucous need to be evaluated before the tantalum bronchographic method can be recommended for use in longitudinal studies (8). Improvements in the method of dust delivery to confine the dust to the conducting airways warrant further study.
The amount of dust insufflated was determined by measuring the dust lost from the injection syringe after insufflation. Animals that survived the dust insufflation received 30- to 50-mg dust. One mouse insufflated with 100-mg dust died 40 min after awaking from the anesthesia.
The diameters measured were confined to the first five generations of airways, because the resolution of the technique limited accurate measurements to airway caliber >0.3 mm. The resolution (100 µm) was determined largely by penumbra blur caused by the 1.8-mm focal spot of the X-ray generator (20). Study of the smaller airways would require a smaller focal spot, similar to that reported in other studies (37).
The MCh dose at the limit in Vm and D measured using graded doses depended on the accumulation of MCh in airway smooth muscle from the previous doses. Thus the limiting dose might be greater in single-dose experiments than in experiments using graded doses. The accumulation of MCh would be reduced by tissue metabolism during the 2–4 min required to take the X-rays between doses.
Our approach using a 10-ms X-ray pulse provided the temporal resolution needed to measure VT in conscious mice breathing at 5 Hz (20). The advantage of the tantalum bronchographic technique over other imaging modalities (1, 7, 26) is the simultaneous measurement of VE, VT, and D in conscious mice breathing at 5 Hz. By contrast, video-assisted plethysmography, limited to images of the body surface, measured VT but neither VE nor D (1). Computed tomographic imaging provided accurate three-dimensional measures of VE and D only in anesthetized animals because of limited temporal resolution (7, 26).
Comparison with Previous Results
In a previous study, the increase in lung volume in response to a single MCh aerosol exposure in conscious mice was independent of dose between 50 and 125 mg/ml and time (1–3 min) of the exposure (20). This behavior was consistent with the relatively small increases in volume measured in the present study between 50 and 100 mg/ml MCh to a maximum value that did not change with three exposures to 100 mg/ml MCh. The previous study showed no change in Raw with a single dose of MCh aerosol between 50 and 125 mg/ml. By contrast, in the present study, graded doses of MCh up to 100 mg/ml had the effect of doubling Raw. A reason for the differences between the two studies is that the insufflation of tantalum dust reduced Raw. Thus Raw values measured after tantalum dust insufflation were smaller than values measured in the absence of tantalum dust (1.7 vs. 3.8 cmH2O·ml–1·s; Ref. 20). This was largely caused by the greater Vm and VT values (0.58 and 0.28 ml) compared with the values measured in the absence of tantalum dust (0.36 and 0.21 ml; Ref. 20).
Raw measured in the present study after tantalum dust insufflation was comparable to values measured using end-inflation occlusion (6) but fourfold greater than values measured using the forced oscillation technique (23). The greater Raw measured by barometric plethysmography was attributed to the combined laminar and turbulent flow contributions to the viscous pressure loss during breathing, whereas the smaller Raw measured by forced oscillation was attributed to the much smaller viscous pressure loss of the imposed laminar flow oscillations alone (20, 21). The relatively high Raw measured by barometric plethysmography was most likely not due to a predominant contribution of the upper airway, because similar high values were measured previously in both nontracheostomized (20) and tracheostomized anesthetized mice (21). However, the contribution of the upper airway to Raw in conscious mice warrants further study.
VE averaged 0.44 ml under control conditions after tantalum dust insufflation and increased to 0.80 ml after MCh aerosol exposure. These values are greater than previous values (20) measured in the absence of tantalum dust (0.25 and 0.51 ml). VT after tantalum dust insufflation averaged 0.28 ml, somewhat greater than values (0.21 ml) measured in the absence of tantalum dust (20). Breathing frequency tended to be higher after tantalum dust insufflation than values in the absence of tantalum dust (6.4 vs. 5.4 Hz). An increased f-induced reduction in tissue resistance might have contributed to the reduced Raw measured after tantalum insufflation (38). A higher VE, VT, and f, and thus ventilation (VT f), after tantalum dust insufflation might point to a reduced diffusing capacity due to tantalum dust deposition on alveolar surfaces. An increase in ventilation would increase the force of breathing generated by an increase in diaphragm contraction that resulted in an increase in lung volume and airway caliber and a reduction in Raw (see Effect of the Increased Raw and Reduced f to the Force of Breathing with MCh). These and other pathophysiological effects of tantalum dust insufflation warrant further study.
Limitation in Raw and D in Response to MCh
The limitation in D in response to MCh aerosol observed in conscious mice in the present study was consistent with the conclusions of studies in normal humans (4, 27, 28, 32, 40, 42) and anesthetized experimental animals (33, 34, 41). The reasons for the limit in constriction are still debated. Several contributing factors to offset maximal airway contractility have been proposed: parenchymal interdependence (13, 24), reduction in airway contractility by cyclic loading (24), mucosal folding (24), and airway-tissue interactions (34). By contrast, one study in anesthetized dogs attributed the measured plateau response to MCh aerosol to dilution effects, because airway closure was observed when MCh solution was applied directly to the airway lumen (3). However, aerosol dilution was most likely not the reason for the limit in constriction, because three 1-min exposures to 100 mg/ml MCh aerosol caused airway closure in anesthetized mice (20) but not in conscious mice of the present study.
Effects of Parenchymal Interdependence
In general, breathing at a higher lung volume increased the expansile forces acting on the airways due to parenchymal interdependence (2, 3, 4, 11, 13, 19, 24, 25, 28, 29, 32–34, 36, 40–42). In the present study, the limiting VE (0.80 ml) in response to MCh was equivalent to a Ptp of 8.6 cmH2O based on the P-V curve of the isolated lungs. This value is slightly higher than 7.5 cmH2O, the minimum Ptp required for parenchymal interdependence to effectively prevent airway closure in isolated dog lungs (13) and in living dogs (41) and the plateau value for the mean lung static recoil measured in normal humans in response to MCh aerosol (28).
Analysis of Airway Contractile Force and Minimum Limiting Diameter in Response to MCh
The airway contractile force (Pc) in response to MCh was calculated by summing two effects: the parenchymal distending force that resisted the airway constriction, and the reduction in the airway elastic recoil produced by the constriction.
Parenchymal distending force resisting airway constriction.
The parenchymal distending force [peribronchial pressure (Px) relative to Ppl] that resisted airway constriction in response to MCh was estimated as follows. We used the pressure-diameter (P-D) behavior of the lung parenchyma surrounding airways (13) and blood vessels (18) that relates Px to the fractional change (Du/Du) in the uniform parenchymal diameter (Du) and the parenchymal shear modulus (µ):
 | (10) |
Du/Du, we assumed that the parenchyma surrounding the airway was uniformly expanded under control conditions (that is, Du = D at 3 cmH2O end-expiratory Ptp) with Px equal to Ppl, and for a uniformly inflated lung Du varied as VL1/3. With MCh, Du/Du was greater in magnitude than D/D, because VL and thus Du increased. With 25 mg/ml MCh, VL increased to 0.96 ml from the control of 0.75 ml, and Du increased by 9%. The 9% correction to the measured D/D of –0.18 (Fig. 2) produced a Du/Du of –0.25. The latter value in Eq. 10 with a µ of 5.3 cmH2O, based on the measured VE of 0.74 ml and end-expiratory Ptp of 7.6 cmH2O (Fig. 4), produced a Px of –3.6 cmH2O. With 100 mg/ml MCh, VL increased to 1.05 ml from the control of 0.75 ml, and Du increased by 12%. The 12% correction to the measured D/D of –0.24 produced a Du/Du of –0.32. The latter value with a µ of 6.0 cmH2O, based on the measured VE of 0.80 ml and end-expiratory Ptp of 8.6 cmH2O, produced a Px of –5.7 cmH2O. In summary, Px that resisted the airway constriction decreased from a control value of 0 cmH2O to –3.6 and –5.7 cmH2O with 25 and 100 mg/ml MCh, respectively (Fig. 5).
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Pel) from end-expiratory Ptp values of 7.6 and 8.6 cmH2O before constriction to Pel of 0.1 and –0.1 cmH2O after constriction were –7.5 and –8.7 cmH2O, respectively. These Pel values, virtually equal in magnitude to the Ptp values, were greater in magnitude than the Px values (–3.6 and –5.7 cmH2O). Thus airway elastic recoil provided the major resistance to airway constriction in response to MCh.
Pc, maximal contractile force, and minimum limiting diameter.
The total Pc, equal to –(Px + Pel), was 11.1 and 14.4 cmH2O with 25 and 100 mg/ml MCh, respectively. Figure 5 is a summary plot of diameter (%Dmax) vs. Pel for the excised airway and the calculated values of –Px, –Pel, and Pc. Also shown are the data of Gunst and Stropp (12) for the active pressure [maximum contractile force (Pmax)] and passive pressure (Pel) measured at fixed volumes in large-dog airway segments. The diameter for each Pmax was obtained by matching its passive pressure to Pel of the excised Pel-D curve. Note that Pmax decreased, whereas Pc increased as diameter was reduced. The intersection of the Pmax-D and Pc-D curves determined the limiting diameter at which Pc equaled Pmax. With 25 mg/ml MCh, Pc (11.1 cmH2O) was much smaller than Pmax (22 cmH2O), which indicated a submaximal response. By contrast with 100 mg/ml MCh, Pc (14.4 cmH2O) was almost equal to Pmax (15 cmH2O) and was virtually a maximal response. The maximal response occurred at the limiting diameter (74% Dmax) slightly below the relaxed diameter at 0-cmH2O Pel. Evidently, the limiting diameter with 100 mg/ml MCh was a minimum, because a smaller diameter with a higher dose would result in a Pc greater than Pmax, which was not physically possible.
The small constriction associated with the limiting diameter was the result of the contractile property that Pmax was sharply reduced with decreasing diameter below 0-cmH2O Pel. However, this property was found for large- but not small-dog airways (12). Thus other factors might prevent airway closure in small airways. A relatively greater constriction consistent with airway closure was estimated based on the maximum constriction measured in vitro (39) and modeling of parenchymal interdependence (13, 24). The P-D and contractile properties of both large and small airways of mice warrant further study.
Effects of Cyclic Loading
One factor that might prevent airway closure in response to MCh was the bronchodilatory effect of a deep inspiration (2, 11, 17, 29, 30). Breathing at an increased VE with a normal VT might result in conditions associated with deep inspirations. For example, the end-inspiratory volume (VE + VT) measured with 100 mg/ml MCh averaged 1.1 ml (Table 1), equivalent to an end-inspiratory Ptp of 15 cmH2O (Fig. 4), conditions that might produce the bronchodilatory effect of a deep inspiration. A bronchodilatory effect on the airway smooth muscle in conscious mice breathing at an elevated lung volume might be related to the reduced contractility measured in response to cyclic changes in muscle length (9). The mechanisms responsible for the time-dependent smooth muscle contractility in airways have been reviewed (10).
Effects of MCh on sighing. To provide evidence for the bronchodilatory effects of deep inspirations, we measured the number of sighs during the 2–4 min that the box was sealed after the exposures to MCh. A sigh was judged to occur when a Pb excursion increased at least 30% above the prior steady-state value. A 30% increase in Pb excursion with MCh was equivalent to an increase in the end-inspiratory volume of 66% VT from 1.1 to 1.29 ml lung air volume; that is, an increase in the end-inspiratory Ptp from 15 to 20 cmH2O (Fig. 4). The depth of the sighs, measured as the fractional change in Pb excursion, did not change with MCh dose and averaged 42 ± 3.9% for the six doses. Figure 6 shows the rate of sighing (sighs/min) vs. C. Linear regression of the data was as follows: sigh rate = 0.017 C + 0.46, R2 = 0.27, n = 24, P = 0.0093. Note that sigh rate increased with dose to a maximum with 100 mg/ml MCh, suggesting that sighing might have contributed to reducing the MCh-induced contractility. However, sigh rate did not change with the two repeated doses of 100 mg/ml MCh. Thus sighing alone most likely did not determine the limit in constriction (Fig. 2), because sigh rate should increase to offset an increase in contractility. Moreover, ventilation (VT f) decreased with dose to a limit with 100 mg/ml MCh. Thus the increased sighing might be a response to hypercapnia. This effect needs to be evaluated.
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The increase in Raw, together with the decrease in f measured in conscious mice in response to MCh, required an increased force generated by the diaphragm with breathing (21). An estimate of the increased force of breathing with MCh follows. The force of breathing is reflected in the Ppl that balances the lung static recoil (Ptp) and the alveolar driving pressure (PA) needed for airway flow (). For sinusoidal flow PA, the amplitude of PA, is due to gas compression (Pg = PA) and is equal to the viscous pressure loss (Raw ; Ref. 21). A measure of the force of breathing Ppl is related to PA and Ptp by the following equation analogous to Eq. 3 (21):
 | (11) |
of 5.6 ml/s (f VT with VT of 0.28 ml and f of 6.4 Hz), PA was 9.5 cmH2O. With Ptp of 2 cmH2O based on VT/2 and the P-V curve, Ppl from Eq. 11 was 9.7 cmH2O, only slightly greater than PA. With MCh, Raw doubled to 3.4 cmH2O·ml–1·s, and with of 3.7 ml/s (VT of 0.29 ml and f of 4.1 Hz), PA increased to 12.2 cmH2O. With MCh, Ptp increased to 3 cmH2O and Ppl increased slightly above PA to 12.6 cmH2O. Thus the force of breathing was due largely to PA and increased minimally by 30% with MCh because the contribution of the twofold increase in Raw to PA was offset largely by the 35% reduction in due to the reduced f. The relatively small value (12 cmH2O) for the force of breathing as reflected by PA in conscious mice in response to MCh contrasts to the much larger value (32 cmH2O) estimated in the anesthetized mice that became apneic after airway closure resulted in diaphragm fatigue and failure (20).
The foregoing analysis was based on Raw computed as if the entire viscous loss (PA) was due to laminar flow conditions, although PA contained both laminar and turbulent flow contributions (21). The assumption of turbulent flow conditions produced a 27% greater value for PA (21).
The 24% reduction in D in conjunction with an increase in airway length (LLm 
VLm1/3) due to the 1.4-fold increase in VLm (Table 1) would predict an increase in Raw based on Poiseuille's equation for laminar flow (Raw VLm1/3/D4) of 3.4-fold. The predicted PA ratio with MCh equal to the product of the Raw ratio of 3.4 and ratio of 0.66 was 2.2, 69% greater than the value of 1.3 estimated using the measured twofold increase in Raw and ratio of 0.66.
If the flow were mainly turbulent, as indicated by the fourfold smaller Raw measured with forced oscillation (23), then for turbulent flow PA v2 VLm1/3 2 VLm1/3/A2 with flow velocity amplitude v = /A and airway cross-sectional area A D2. Thus, with a ratio of 0.66, VLm ratio of 1.4, and D ratio of 0.76, PA ratio with MCh was 1.4, close to the value (1.3) estimated using barometric plethysmography. Differences between the PA ratio with MCh predicted using Poiseuille's equation for laminar flow in uniform tubes and the ratio predicted using the assumption of turbulent flow might also reflect nonuniform changes in airway caliber along the tracheobronchial tree.
Concluding Remarks
We developed a tantalum bronchographic method to study the effect of bronchoconstrictor MCh aerosol on airway constriction in conscious mice. Single projection X-ray images of the thorax and lungs insufflated with tantalum dust provided measurements of airway caliber, in addition to VE and VT. Our approach using a 10-ms X-ray pulse provided the temporal resolution needed to reduce image blur due to respiratory and cardiogenic motion in conscious mice breathing at 5 Hz (20). The twofold increase in Raw using barometric plethysmography, together with the 35% reduction in f in response to MCh, required a 30% increase in the force of breathing as measured by PA. The monotonic decrease to a minimum limiting D in response to graded doses of MCh aerosol was attributed primarily to the Raw-induced increases in diaphragm contraction and Ptp that resulted in increases in parenchymal and airway elastic forces to offset Pc, in conjunction with the reduced Pmax that occurred when airway elastic recoil was reduced below zero.
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FOOTNOTES |
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The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
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